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In the given figure, O is the center of the circle. OA = 3 cm, AC = 3 cm and OM ⊥ AC. What is ∠ABC equal to?

(a) 60° 

(b) 45° 

(c) 30° 

(d) None of these

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Answer : (c) 30º

Given OA = 3 cm ⇒ OC = 3 cm (radii of the circle) 

Also AC = 3 cm ⇒ OA = OC = AC ⇒ ∆ AOC is equilateral 

⇒ ∠AOC = 60°.

⇒ ∠ABC = \(\frac{1}{2}\) \(\times\) ∠AOC 

 = 30° (Angle subtended by an arc of a circle at the center is double the angle subtended by it at any point on the remaining part of the circle.)

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